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Vapour-liquid equilibrium in the carbon dioxide—ethyl acetate system at high pressure
Fluid Phase Equilibria, 97 (1994) 119-126
ELSEVIER
Vapour-liquid equilibrium in the carbon dioxide ethyl acetate system at high pressure
Zdenkk Wagner and Jan PavliEek E. H&la Laboratory of Thermodynamics, CZ-165 02 Praha 6 (Czech Republic)
KEYWORDS:
experiments,
Institute of Chemical Process Fundamentals,
data, VLE high pressure, carbon dioxide, esters.
(ReceivedNovember2,1993; acceptedin finalformApril6.1994)
ABSTRACT Wagner Z. and PavEek J.: Vapour-liquid equilibrium in the carbon dioxide system at high pressure. Fluid Phase Equilibria,
ethyl acetate
Vapour-liquid equilibrium data in the carbon dioxide - ethyl acetate system were measured isothermally at 303.15K, 313.15K, and 323.15K at pressures ranging from 2MPa to 9MPa. The experimental data were fitted to the Soave-Redlich-Kwong equation of state adopting a maximum likelihood procedure.
INTRODUCTION Carbon dioxide is a perspective solvent for supercritical fluid extraction. Due to its nontoxicity and low critical temperature it can be used for extracting natural materials, mainly in food and pharmaceutical industry. Carbon dioxide has rather simple molecule with zero dipole and nonzero quadrupole moment. It can be used for development and testing of statistical thermodynamical models. For this purpose experimental data are needed. It is important to have information on vapour-liquid equilibrium of carbon dioxide with different groups of compounds. In this work we selected ethyl acetate as a representative of esters. It can be found from the bibliographical database by Wichterle et al. (1993) that no high-pressure vapour-liquid equilibrium data for this system are available. APPARATUS Measurement of high-pressure vapour-liquid equilibrium was performed in a static apparatus described previously by Wagner and Wichterle (1987) which was slightly modified.
0378-3812/94/.$07.00 @ 1994 - Elsevier Science B.V. All rights reserved SSDZ 0378-3812 (94) 02526-7
120
Z Wagner, .I. PavEek/Fluid
Phase Equilibria 97 (1994) IN-126
Temperature of the equilibrium cell, located in a thermostatted bath, was measured by the Systemteknik S 1220 digital thermometer that was calibrated against a platinum resistance thermometer Leeds & Northrup provided with National Bureau of Standards certificate. The accuracy of temperature measurement was within 0.002K of the temperatures on the ITS-90. ~quilib~um pressure was measured by means of bourdon type Heise pressure gauges with ranges 5 MPa and 10MPa respectively, with declared hysteresis 0.1% of the full scale range and repeatability 0.001 MPa. The investigated system was separated by a pressure transducer manufactured by Ruska Instrument Corp. from an air reference system. The air counterpressure is controlled automatically. Sampling of both phases was based upon the capillary technique developed originally by Lhotak and Wichterle (1981). The latest modification is fully described by PavlEek and Richter (1993). The capillaries were removably connected to a heated mixer where the sample was mixed with the carrier gas. The carrier gas with the dissolved sample flows through the chromatographic six-way sampling valve. The analyses were carried out on the Hewlett-Packard gas chromatograph HP 5880 A using the column packed with 15% l,Z-bis(2-cyanoethoxy)ethane on Chromaton N-AW. Response factors of a thermal conductivity detector were determined by injecting a known amount of pure components. TABLE 1 Experimental data of vapour-Iiquid equilibrium of carbon dioxide with ethyl acetate XC02
T 0.5684 0.7088 0.7104 0.7917 0.8096 0.8518 0.8506 0.8572 0.9110 0.9084 0.9638 0.9930 1.0000
YCOZ = 303.15K 0.9925 2.0316 0.9938 3.0590 0.9939 3.0772 0.9955 3.8503 0.9926 4.0611 0.9941 4.5231 0.9945 4.5424 0.9957 4.6174 0.9942 5.3206 0.9948 5.3591 0.9957 6.3247 0.9969 7.0461 1‘0000 7.2731
xc02
T 0.5356 0.6730 0.7592 0.8024 0.8299 0.8647 0.8590 0.9036 0.9414 0.9483 0.9720 0.9851 0.9886
YCS = 313.15K 0.9858 2.0924 0.9881 3.1198 0.9918 3.8331 0.9901 4.5394 0.9897 4.8585 0.9918 5.4938 0.9917 5.5202 0.9909 6.1677 0.9906 7.0765 0.9946 7.1424 0.9940 7.7382 0.9933 8.1090 0.9919 8.1779
“CO*
T 0.4500 0.4464 0.5733 0.5815 0.6727 0.6739 0.7605 0.7771 0.8159 0.8401 0.8634 0.9052 0.9238 0.9347 0.9473 0.9684
YCO2
= 323.15K 0.9878 2.0468 0.9849 2.0660 0.9900 2.9638 0.9894 3.0529 0.9898 3.9071 0.9897 3.9294 0.9915 4.9639 0.9911 5.2253 0.9884 5.7998 0.9922 6.1727 0.9915 6.6003 0.9893 7.3552 0.9900 7.7605 0.9903 8.0239 0.9889 8.3694 0.9866 8.9065
0.9752 0.9826 9.0200
Z. Wagner, J. PavKek /Fluid Phase Equilibria 97 (I 994) 119-l 26
121
10 P [MPa]
0.2
Fig. 1
0.4
0.6
0.8
1
P-x,y diagram of the carbon dioxide - ethyl acetate system n 313.15K * 323.15K . 303.15K
EXPERIMENTAL Carbon dioxide (Chemical Works Litvinov) was analyzed to have purity greater then 99.9% and was used without further purification. Ethyl acetate (Lachema Brno, Czechoslovakia), p. a., was refluxed with acetic anhydride (about 1 ml per 10 ml of ester) and fractionally distilled on a 30-plate column packed with glass helices. Purity was tested by gas chromate raphy to B be greater than 99.9%; refractive index and liquid density were n293.15K = The literature values as 1.3725 and p2Q3.15K = 0.89458g/cm3, respectively. reported by Timmermans (1950 and 1965) vary from 0.89446 to 0.89468 g/cm3 for the liquid density and from 1.37239 to 1.3728 for the refractive index.
122
Z Wagner, J. PavKek/
Fluid Phase Equilibria 97 (1994) 119-126
Vapour-liquid equilibrium data were measured isothermally. The cell was first evacuated and then filled with the liquid component. The traces of dissolved air were removed by repeated charging the cell with carbon dioxide to pressure about 0.5MPa and evacuation. Afterwards the cell was charged with carbon dioxide to the desired pressure. The contents of the cell were intensively stirred until both temperature and pressure remained constant for 10 minutes. The sampling system was flushed with carrier gas before analysis of each phase. The liquid phase was always analyzed first because it caused smaller pressure drop (approx. 0.002 MPa) than the sampling of the vapour phase. The results of measurement are presented in Table 1 and the P-x,y diagram is depicted in Figure 1. DATA REDUCTION The Soave-Redlich-Kwong form (Soave, 1972) 1 Z=m-bp-(l
equation of state is traditionally
written in the
ap +bp)’
However, the parameter a is temperature dependent and therefore the classical mixing rule for a does not mix constants. We therefore adopt the method suggested by Kwak and Mansoori (1986) wh ic h was used by Wagner and PavliEek (1993). Equation 1 is then rewritten into the form 2=--P 1
c/(RT)
1
+ d - 2 dm
(2)
1 +bp
where c and d are temperature independent parameters which stem from the expansion of the temperature dependence of a. The constants of the mixture are evaluated from b =
C&Xj(li
C
=
lkij)
[(bf'3
+
bj'/")
/
21” )
~~~i~j(l-kj)~~
d = C Cxixj i
(3)
j
(1 - mij) [ (d,“3 + di’3) / 21”
(4)
(5)
j
where kij, Zij, and m;j are interaction parameters and the pure components constants are obtained from the critical properties and the acentric factor using the modification proposed by Graboski and Daubert (1978). bj = 0.086644 R Tci/P,i ,
(6)
Z Wagner, .I. PavliEek/ Fluid Phase Equilibria 97 (1994) IN-126
123
TABLE 2 Critical properties’and acentric factors of pure components Component carbon dioxide ethyl acetate
4i = 4
=
W
304.10 523.20
7.375 3.830
0.239 0.362
(8) (9)
0.42742 R2 Ti/P,i, 0.48508 + 1.55171 wi - 0.15613 wp .
(10)
The modification by Graboski and Daubert (Eqn. 10) differs from the original version in numerical constants. Graboski and Daubert evaluated them from the temperature dependence of vapour pressures of pure hydrocarbons. Therefore we prefer this equation to the original version of Soave. However, it will not influence the quality of fit, it only may slightly change the values of the interaction parameters. The critical constants and acentric factors of the pure components were taken from Ambrose and Townsend (1978) and are summarized in Table 2. TABLE 3 Results of fitting the vapour-liquid equilibrium data to the Soave-Redlich-Kwong of state A = experimental - calculated xc02
Axcoa
YCOZ
AYCO,
AT WI
0.5676 0.7182 0.7202 0.7929 0.8095 0.8433 0.8446 0.8497 0.8945 0.8967 0.9534 0.9930 0.9977
0.9898 303.146
0.9941 0.9941 0.9958 0.9962 0.9968 0.9969 0.9969 0.9977 0.9977 0.9985 0.9993 0.9996
303.150 303.150 303.150 303.153 303.151 303.151 303.150 303.149 303.150 303,138 303.154 303.209
2.0382 3.0582 3.0764 3.8500 4.0589 4.5228 4.5420 4.6178 5.3244 5.3614 6.3420 7.0434 7.1572
0.00078 -0.00944 -0.00983 -0.00124 0.00007 0.00852 0.00601 0.00745 0.01649 0.01168 0.01037 -0.00004 0.00234
0.00272 -0.00027 -0.00023 -0.00035 -0.00359 -0.00273 -0.00236 -0.00125 -0.00346 -0.00290 -0.00276 -0.00236 0.00042
0.004 -0.000 -0.000 -0.000 -0.003 -0.001 -0.001 -0.000 0.000 0.000 0.012 -0.004 -0.059
-0.0066 0.0008 0.0008 0.0003 0.0022 0.0003 0.0004 -0.0004 -0.0038 -0.0023 -0.0173 0.0027 0.1159
continued on the next page
equation
WO,
YCOZ
P
[MPa] 0.5097 0.9835 313.1472.0972 0.6664OS9895 313.1513.1185 0.73640.9918 313.1503.8344 0.79010.9934 313.1534.5379 0.81120.9939 313.1534.8577 0.84900.9948 313.1525.4944 0.85040.9948 313.1525.5199 0.88470.9954313.1526.1705 0.92840.9958313.1507.083% 0.93170.9959313.1437.1538 0.96010.9957313.1287.7672 0.98510.9942313.1508.2766 0.98640.9939313.1508.2982
Axcoa
Lfigtcoz
AT
Kl 0.02595 0.00234 0.003-0.0048 0.00663-0.00136-0.001 0.0013 0.02280-0~00004 0.000-0.0013 0.01234-0.00330-0.003 0.0015 0.01870-0.00423-0.003 0.~08 0.01567-0.00297-0.002 -0.0006 0.00856-0.00309-0.002 0.0003 0.01890-0.00448-0.002 -0.0028 0.01297-0.00524 0.000-0.0067 0.01657-0.00125 0.007-0.0114 0.01189-0.00175 0.022-0.0290 0.00000-0.00087 0.000-0.1676 0.00220-0.00197 0.000-0.1203
0.44130.9741323.1242.0894 0.00869 0.01370 0.026-0.0426 0.44090.9741323.1372.0880 0.00549 0.01083 0.013-0.0220 0.59400.9817323.1322.9840-0.02070 0.00825 0.018-0.0202 0.60450.9823323.1373.0675-0.02304 0.00714 0.013-0.0146 0.69170.9863323.1443.9114-0.01899 0.00354 0.006-0.0043 0.69360.9863323.1453.9333-0.01969 0.00336 0.005 -0.0039 0.76960.9892323.1474.9654-0.00912 0.00226 0.003-0.0015 0.78560.9897323.1485.2259-0.00855 0.00135 0.002-0.0006 0.81780.9906323.1525.7989-0.00189-0.00224-0.002 0.0009 0.83690.9911323.1486.1734 0.00315 0~00113 Yl.002-0.0007 0.85740.9914323.1506.6009 0.00603 0.00007 0.000-0.0006 0.89070.9917323.1517.3580 0.01451-0.00241-0.000 -0.0028 0.90760.9916323.1497.7654 0.01624-0.00162 0.001-0.0049 0.91830.9915323.1478.0306 0.01640-0.00115 0.003-0.0067 0.93230.9910323.~468.3796 0.01501-0.00210 0.004 -0.0102 0.95510.9892323.1338.9332 0.01331-0.00257 0.017-0.0267 0.96140.9882323.1149.0724 0.01380-0.00556 0.036 -0.0524 Parameters: kls= -0.46222, 112 = -0.05052, ml2= 0.40471 All variables are determined experiment~ly and therefore they cannot be errorless, We could afford to neglect errors in temperature but the errors in the composition of both phases are almost the same. For this reason we adopt maximum likelihood procedure assuming that the measurement errors in all variables are additive and uncorrelated, possessing normal distribution with zero mean and known variance obtained from the analysis of the precision of me~urement, The parameters are then determined by means of an iterative procedure proposed by Rod and Han61 (1980).
Z. Wagner, J. PavlfCek / Fluid Phase Equilibria 97 (1994) 119-l 26
125
DISCUSSION The results of the fit is shown in Table 3. The solid lines in Figure 1 represent the isotherms calculated using the interaction parameters kiz, 112, and ml2 obtained from the correlation. It can be seen that the agreement is quite good, only the calculated critical presure for 323.15 K is higher than the experimental value. ACKNOWLEDGMENT The authors would like to acknowledge the partial support of the AIF Project No. 9280 and the Grant Agency of the Czechoslovak Academy of Sciencesgrant No. 47218. LIST OF SYMBOLS Latin letters a, b, c, d parameters
Ic, I, m P R T 2
Y Z
of the Soave-Redlich-Kwong interaction parameters pressure universal gas constant temperature liquid mole fraction vapour mole fraction compressibility factor
equation of state
Greek letters
44 W
parameters defined by equations acentric factor
10 and 9, respectively
Subscripts c
i,.i
critical property related to the i-th or j-th component,
respectively
REFERENCES Ambrose D. and Townsend R., 1978. Vapour-liquid critical properties. National Physical Laboratory, Teddington. Graboski M. S. and Daubert T. E., 1978. A modified Soave equation of state for phase equilibrium calculations. I. Hydrocarbon systems. Ind. Eng. Chem., Proc. Des. Dev., 17: 443-448. Kwak T. Y. and Mansoori G. A., 1986. Van der Wards mixing rules for cubic equations of state. Application for supercritical fluid extraction modelling. Chem. Eng. Sci., 41: 1303-1309.
126
2. Wagner, J. PavliCek/ Fluid Phase Equilibria 97 (1994) 119426
Lhot&k V. and Wichterle I., 1981. Vapour-liquid equilibrium in the ethane - n-butane systems at high pressures. Fluid Phase Equil., 6: 229-235. PavliEek J. and Richter M., 1993. High pressure vapour-liquid equilibrium in the carbon dioxide - o-pinene system. Fluid Phase Equil., 90: 125-133. Rod V. and HanEil V., 1980. Iterative estimation of model parameters when measurements of all variables are subject to errors. Comput. Chem. Eng., 4: 33-38. Soave G., 1972. Equilibrium constants from a modified Redlich-Kwong equation of state. Chem. Eng. Sci., 27: 1197-1203. Timmermans J., 1950. Physico-Chemical Constants of Pure Organic Compounds, Vol. 1. Elsevier, Amsterdam. Timmermans J., 1965. Physico-Chemical Constants of Pure Organic Compounds, Vol. 2. Elsevier, Amsterdam. Wagner Z. and Pavlizek J., 1993. Vapour-liquid equilibrium in the carbon dioxide - p-cymene system at high pressure. Fluid Phase Equil., 90: 135-141. Wagner 2. and Wichterle I., 1987. High-pressure vapour-liquid equilibrium in systems containing carbon dioxide, 1-hexene, and n-hexane. Fluid Phase Equil., 33: 109-123. Wichterle I., Linek J., Wagner Z., Kehiaian H. V., 1993. Vapor-Liquid Equilibrium Bibliographic Database. ELDATA SARL, Montreuil.
ELSEVIER
Vapour-liquid equilibrium in the carbon dioxide ethyl acetate system at high pressure
Zdenkk Wagner and Jan PavliEek E. H&la Laboratory of Thermodynamics, CZ-165 02 Praha 6 (Czech Republic)
KEYWORDS:
experiments,
Institute of Chemical Process Fundamentals,
data, VLE high pressure, carbon dioxide, esters.
(ReceivedNovember2,1993; acceptedin finalformApril6.1994)
ABSTRACT Wagner Z. and PavEek J.: Vapour-liquid equilibrium in the carbon dioxide system at high pressure. Fluid Phase Equilibria,
ethyl acetate
Vapour-liquid equilibrium data in the carbon dioxide - ethyl acetate system were measured isothermally at 303.15K, 313.15K, and 323.15K at pressures ranging from 2MPa to 9MPa. The experimental data were fitted to the Soave-Redlich-Kwong equation of state adopting a maximum likelihood procedure.
INTRODUCTION Carbon dioxide is a perspective solvent for supercritical fluid extraction. Due to its nontoxicity and low critical temperature it can be used for extracting natural materials, mainly in food and pharmaceutical industry. Carbon dioxide has rather simple molecule with zero dipole and nonzero quadrupole moment. It can be used for development and testing of statistical thermodynamical models. For this purpose experimental data are needed. It is important to have information on vapour-liquid equilibrium of carbon dioxide with different groups of compounds. In this work we selected ethyl acetate as a representative of esters. It can be found from the bibliographical database by Wichterle et al. (1993) that no high-pressure vapour-liquid equilibrium data for this system are available. APPARATUS Measurement of high-pressure vapour-liquid equilibrium was performed in a static apparatus described previously by Wagner and Wichterle (1987) which was slightly modified.
0378-3812/94/.$07.00 @ 1994 - Elsevier Science B.V. All rights reserved SSDZ 0378-3812 (94) 02526-7
120
Z Wagner, .I. PavEek/Fluid
Phase Equilibria 97 (1994) IN-126
Temperature of the equilibrium cell, located in a thermostatted bath, was measured by the Systemteknik S 1220 digital thermometer that was calibrated against a platinum resistance thermometer Leeds & Northrup provided with National Bureau of Standards certificate. The accuracy of temperature measurement was within 0.002K of the temperatures on the ITS-90. ~quilib~um pressure was measured by means of bourdon type Heise pressure gauges with ranges 5 MPa and 10MPa respectively, with declared hysteresis 0.1% of the full scale range and repeatability 0.001 MPa. The investigated system was separated by a pressure transducer manufactured by Ruska Instrument Corp. from an air reference system. The air counterpressure is controlled automatically. Sampling of both phases was based upon the capillary technique developed originally by Lhotak and Wichterle (1981). The latest modification is fully described by PavlEek and Richter (1993). The capillaries were removably connected to a heated mixer where the sample was mixed with the carrier gas. The carrier gas with the dissolved sample flows through the chromatographic six-way sampling valve. The analyses were carried out on the Hewlett-Packard gas chromatograph HP 5880 A using the column packed with 15% l,Z-bis(2-cyanoethoxy)ethane on Chromaton N-AW. Response factors of a thermal conductivity detector were determined by injecting a known amount of pure components. TABLE 1 Experimental data of vapour-Iiquid equilibrium of carbon dioxide with ethyl acetate XC02
T 0.5684 0.7088 0.7104 0.7917 0.8096 0.8518 0.8506 0.8572 0.9110 0.9084 0.9638 0.9930 1.0000
YCOZ = 303.15K 0.9925 2.0316 0.9938 3.0590 0.9939 3.0772 0.9955 3.8503 0.9926 4.0611 0.9941 4.5231 0.9945 4.5424 0.9957 4.6174 0.9942 5.3206 0.9948 5.3591 0.9957 6.3247 0.9969 7.0461 1‘0000 7.2731
xc02
T 0.5356 0.6730 0.7592 0.8024 0.8299 0.8647 0.8590 0.9036 0.9414 0.9483 0.9720 0.9851 0.9886
YCS = 313.15K 0.9858 2.0924 0.9881 3.1198 0.9918 3.8331 0.9901 4.5394 0.9897 4.8585 0.9918 5.4938 0.9917 5.5202 0.9909 6.1677 0.9906 7.0765 0.9946 7.1424 0.9940 7.7382 0.9933 8.1090 0.9919 8.1779
“CO*
T 0.4500 0.4464 0.5733 0.5815 0.6727 0.6739 0.7605 0.7771 0.8159 0.8401 0.8634 0.9052 0.9238 0.9347 0.9473 0.9684
YCO2
= 323.15K 0.9878 2.0468 0.9849 2.0660 0.9900 2.9638 0.9894 3.0529 0.9898 3.9071 0.9897 3.9294 0.9915 4.9639 0.9911 5.2253 0.9884 5.7998 0.9922 6.1727 0.9915 6.6003 0.9893 7.3552 0.9900 7.7605 0.9903 8.0239 0.9889 8.3694 0.9866 8.9065
0.9752 0.9826 9.0200
Z. Wagner, J. PavKek /Fluid Phase Equilibria 97 (I 994) 119-l 26
121
10 P [MPa]
0.2
Fig. 1
0.4
0.6
0.8
1
P-x,y diagram of the carbon dioxide - ethyl acetate system n 313.15K * 323.15K . 303.15K
EXPERIMENTAL Carbon dioxide (Chemical Works Litvinov) was analyzed to have purity greater then 99.9% and was used without further purification. Ethyl acetate (Lachema Brno, Czechoslovakia), p. a., was refluxed with acetic anhydride (about 1 ml per 10 ml of ester) and fractionally distilled on a 30-plate column packed with glass helices. Purity was tested by gas chromate raphy to B be greater than 99.9%; refractive index and liquid density were n293.15K = The literature values as 1.3725 and p2Q3.15K = 0.89458g/cm3, respectively. reported by Timmermans (1950 and 1965) vary from 0.89446 to 0.89468 g/cm3 for the liquid density and from 1.37239 to 1.3728 for the refractive index.
122
Z Wagner, J. PavKek/
Fluid Phase Equilibria 97 (1994) 119-126
Vapour-liquid equilibrium data were measured isothermally. The cell was first evacuated and then filled with the liquid component. The traces of dissolved air were removed by repeated charging the cell with carbon dioxide to pressure about 0.5MPa and evacuation. Afterwards the cell was charged with carbon dioxide to the desired pressure. The contents of the cell were intensively stirred until both temperature and pressure remained constant for 10 minutes. The sampling system was flushed with carrier gas before analysis of each phase. The liquid phase was always analyzed first because it caused smaller pressure drop (approx. 0.002 MPa) than the sampling of the vapour phase. The results of measurement are presented in Table 1 and the P-x,y diagram is depicted in Figure 1. DATA REDUCTION The Soave-Redlich-Kwong form (Soave, 1972) 1 Z=m-bp-(l
equation of state is traditionally
written in the
ap +bp)’
However, the parameter a is temperature dependent and therefore the classical mixing rule for a does not mix constants. We therefore adopt the method suggested by Kwak and Mansoori (1986) wh ic h was used by Wagner and PavliEek (1993). Equation 1 is then rewritten into the form 2=--P 1
c/(RT)
1
+ d - 2 dm
(2)
1 +bp
where c and d are temperature independent parameters which stem from the expansion of the temperature dependence of a. The constants of the mixture are evaluated from b =
C&Xj(li
C
=
lkij)
[(bf'3
+
bj'/")
/
21” )
~~~i~j(l-kj)~~
d = C Cxixj i
(3)
j
(1 - mij) [ (d,“3 + di’3) / 21”
(4)
(5)
j
where kij, Zij, and m;j are interaction parameters and the pure components constants are obtained from the critical properties and the acentric factor using the modification proposed by Graboski and Daubert (1978). bj = 0.086644 R Tci/P,i ,
(6)
Z Wagner, .I. PavliEek/ Fluid Phase Equilibria 97 (1994) IN-126
123
TABLE 2 Critical properties’and acentric factors of pure components Component carbon dioxide ethyl acetate
4i = 4
=
W
304.10 523.20
7.375 3.830
0.239 0.362
(8) (9)
0.42742 R2 Ti/P,i, 0.48508 + 1.55171 wi - 0.15613 wp .
(10)
The modification by Graboski and Daubert (Eqn. 10) differs from the original version in numerical constants. Graboski and Daubert evaluated them from the temperature dependence of vapour pressures of pure hydrocarbons. Therefore we prefer this equation to the original version of Soave. However, it will not influence the quality of fit, it only may slightly change the values of the interaction parameters. The critical constants and acentric factors of the pure components were taken from Ambrose and Townsend (1978) and are summarized in Table 2. TABLE 3 Results of fitting the vapour-liquid equilibrium data to the Soave-Redlich-Kwong of state A = experimental - calculated xc02
Axcoa
YCOZ
AYCO,
AT WI
0.5676 0.7182 0.7202 0.7929 0.8095 0.8433 0.8446 0.8497 0.8945 0.8967 0.9534 0.9930 0.9977
0.9898 303.146
0.9941 0.9941 0.9958 0.9962 0.9968 0.9969 0.9969 0.9977 0.9977 0.9985 0.9993 0.9996
303.150 303.150 303.150 303.153 303.151 303.151 303.150 303.149 303.150 303,138 303.154 303.209
2.0382 3.0582 3.0764 3.8500 4.0589 4.5228 4.5420 4.6178 5.3244 5.3614 6.3420 7.0434 7.1572
0.00078 -0.00944 -0.00983 -0.00124 0.00007 0.00852 0.00601 0.00745 0.01649 0.01168 0.01037 -0.00004 0.00234
0.00272 -0.00027 -0.00023 -0.00035 -0.00359 -0.00273 -0.00236 -0.00125 -0.00346 -0.00290 -0.00276 -0.00236 0.00042
0.004 -0.000 -0.000 -0.000 -0.003 -0.001 -0.001 -0.000 0.000 0.000 0.012 -0.004 -0.059
-0.0066 0.0008 0.0008 0.0003 0.0022 0.0003 0.0004 -0.0004 -0.0038 -0.0023 -0.0173 0.0027 0.1159
continued on the next page
equation
WO,
YCOZ
P
[MPa] 0.5097 0.9835 313.1472.0972 0.6664OS9895 313.1513.1185 0.73640.9918 313.1503.8344 0.79010.9934 313.1534.5379 0.81120.9939 313.1534.8577 0.84900.9948 313.1525.4944 0.85040.9948 313.1525.5199 0.88470.9954313.1526.1705 0.92840.9958313.1507.083% 0.93170.9959313.1437.1538 0.96010.9957313.1287.7672 0.98510.9942313.1508.2766 0.98640.9939313.1508.2982
Axcoa
Lfigtcoz
AT
Kl 0.02595 0.00234 0.003-0.0048 0.00663-0.00136-0.001 0.0013 0.02280-0~00004 0.000-0.0013 0.01234-0.00330-0.003 0.0015 0.01870-0.00423-0.003 0.~08 0.01567-0.00297-0.002 -0.0006 0.00856-0.00309-0.002 0.0003 0.01890-0.00448-0.002 -0.0028 0.01297-0.00524 0.000-0.0067 0.01657-0.00125 0.007-0.0114 0.01189-0.00175 0.022-0.0290 0.00000-0.00087 0.000-0.1676 0.00220-0.00197 0.000-0.1203
0.44130.9741323.1242.0894 0.00869 0.01370 0.026-0.0426 0.44090.9741323.1372.0880 0.00549 0.01083 0.013-0.0220 0.59400.9817323.1322.9840-0.02070 0.00825 0.018-0.0202 0.60450.9823323.1373.0675-0.02304 0.00714 0.013-0.0146 0.69170.9863323.1443.9114-0.01899 0.00354 0.006-0.0043 0.69360.9863323.1453.9333-0.01969 0.00336 0.005 -0.0039 0.76960.9892323.1474.9654-0.00912 0.00226 0.003-0.0015 0.78560.9897323.1485.2259-0.00855 0.00135 0.002-0.0006 0.81780.9906323.1525.7989-0.00189-0.00224-0.002 0.0009 0.83690.9911323.1486.1734 0.00315 0~00113 Yl.002-0.0007 0.85740.9914323.1506.6009 0.00603 0.00007 0.000-0.0006 0.89070.9917323.1517.3580 0.01451-0.00241-0.000 -0.0028 0.90760.9916323.1497.7654 0.01624-0.00162 0.001-0.0049 0.91830.9915323.1478.0306 0.01640-0.00115 0.003-0.0067 0.93230.9910323.~468.3796 0.01501-0.00210 0.004 -0.0102 0.95510.9892323.1338.9332 0.01331-0.00257 0.017-0.0267 0.96140.9882323.1149.0724 0.01380-0.00556 0.036 -0.0524 Parameters: kls= -0.46222, 112 = -0.05052, ml2= 0.40471 All variables are determined experiment~ly and therefore they cannot be errorless, We could afford to neglect errors in temperature but the errors in the composition of both phases are almost the same. For this reason we adopt maximum likelihood procedure assuming that the measurement errors in all variables are additive and uncorrelated, possessing normal distribution with zero mean and known variance obtained from the analysis of the precision of me~urement, The parameters are then determined by means of an iterative procedure proposed by Rod and Han61 (1980).
Z. Wagner, J. PavlfCek / Fluid Phase Equilibria 97 (1994) 119-l 26
125
DISCUSSION The results of the fit is shown in Table 3. The solid lines in Figure 1 represent the isotherms calculated using the interaction parameters kiz, 112, and ml2 obtained from the correlation. It can be seen that the agreement is quite good, only the calculated critical presure for 323.15 K is higher than the experimental value. ACKNOWLEDGMENT The authors would like to acknowledge the partial support of the AIF Project No. 9280 and the Grant Agency of the Czechoslovak Academy of Sciencesgrant No. 47218. LIST OF SYMBOLS Latin letters a, b, c, d parameters
Ic, I, m P R T 2
Y Z
of the Soave-Redlich-Kwong interaction parameters pressure universal gas constant temperature liquid mole fraction vapour mole fraction compressibility factor
equation of state
Greek letters
44 W
parameters defined by equations acentric factor
10 and 9, respectively
Subscripts c
i,.i
critical property related to the i-th or j-th component,
respectively
REFERENCES Ambrose D. and Townsend R., 1978. Vapour-liquid critical properties. National Physical Laboratory, Teddington. Graboski M. S. and Daubert T. E., 1978. A modified Soave equation of state for phase equilibrium calculations. I. Hydrocarbon systems. Ind. Eng. Chem., Proc. Des. Dev., 17: 443-448. Kwak T. Y. and Mansoori G. A., 1986. Van der Wards mixing rules for cubic equations of state. Application for supercritical fluid extraction modelling. Chem. Eng. Sci., 41: 1303-1309.
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2. Wagner, J. PavliCek/ Fluid Phase Equilibria 97 (1994) 119426
Lhot&k V. and Wichterle I., 1981. Vapour-liquid equilibrium in the ethane - n-butane systems at high pressures. Fluid Phase Equil., 6: 229-235. PavliEek J. and Richter M., 1993. High pressure vapour-liquid equilibrium in the carbon dioxide - o-pinene system. Fluid Phase Equil., 90: 125-133. Rod V. and HanEil V., 1980. Iterative estimation of model parameters when measurements of all variables are subject to errors. Comput. Chem. Eng., 4: 33-38. Soave G., 1972. Equilibrium constants from a modified Redlich-Kwong equation of state. Chem. Eng. Sci., 27: 1197-1203. Timmermans J., 1950. Physico-Chemical Constants of Pure Organic Compounds, Vol. 1. Elsevier, Amsterdam. Timmermans J., 1965. Physico-Chemical Constants of Pure Organic Compounds, Vol. 2. Elsevier, Amsterdam. Wagner Z. and Pavlizek J., 1993. Vapour-liquid equilibrium in the carbon dioxide - p-cymene system at high pressure. Fluid Phase Equil., 90: 135-141. Wagner 2. and Wichterle I., 1987. High-pressure vapour-liquid equilibrium in systems containing carbon dioxide, 1-hexene, and n-hexane. Fluid Phase Equil., 33: 109-123. Wichterle I., Linek J., Wagner Z., Kehiaian H. V., 1993. Vapor-Liquid Equilibrium Bibliographic Database. ELDATA SARL, Montreuil.